Suppose we want to test(i) whether two independent samples xi, (i = 1, 2, …..,n1) and yj, (j = 1, 2, …n2) have been drawn from the normal populations with the same variance σ2, or (ii) whether the two independent estimates of the population variance are homogeneous or not.
Under the null hypothesis (H0) that (i) σX2 = σY2 = σ2 , that is the population variances are equal or (ii) two independent estimates of the population variance are homogeneous, the statistic F is given by
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